0002.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ {x} = 2 \, {y} + {x'} \hspace{2em}x(0)= 3 \]\[ -{y'} = -6 \, {y} - 2 \, {x} \hspace{2em}x(0)= -3 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= e^{\left(5 \, t\right)} + 2 \, e^{\left(2 \, t\right)} \]\[y= -2 \, e^{\left(5 \, t\right)} - e^{\left(2 \, t\right)} \]
\end{exerciseAnswer}